Intensity-coupled Polarization in Instruments with a Continuously Rotating Half-wave Plate

We discuss a systematic effect associated with measuring polarization with a continuously rotating half-wave plate. The effect was identified with the data from the E and B Experiment (EBEX), which was a balloon-borne instrument designed to measure the polarization of the CMB as well as that from Galactic dust. The data show polarization fraction larger than 10\% while less than 3\% were expected from instrumental polarization. We give evidence that the excess polarization is due to detector non-linearity in the presence of a continuously rotating HWP. The non-linearity couples intensity signals into polarization. We develop a map-based method to remove the excess polarization. Applying this method for the 150 (250) GHz bands data we find that 81\% (92\%) of the excess polarization was removed. Characterization and mitigation of this effect is important for future experiments aiming to measure the CMB B-modes with a continuously rotating HWP.